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Stability and stabilization of a class of fractional-order nonlinear systems for \(\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\)

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Abstract

This paper investigates the stability and stabilization problem of fractional-order nonlinear systems for \(0<\alpha <2\). Based on the fractional-order Lyapunov stability theorem, S-procedure and Mittag–Leffler function, the stability conditions that ensure local stability and stabilization of a class of fractional-order nonlinear systems under the Caputo derivative with \(0<\alpha <2\) are proposed. Finally, typical instances, including the fractional-order nonlinear Chen system and the fractional-order nonlinear Lorenz system, are implemented to demonstrate the feasibility and validity of the proposed method.

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Acknowledgements

This work was supported by the scientific research foundation of the National Natural Science Foundation (Grant Numbers 51509210 and 51479173), Shaanxi province science and technology plan (Grant Number 2016KTZDNY-01-01), the Science and Technology Project of Shaanxi Provincial Water Resources Department (Grant Number 2015slkj-11), the International Cooperation Project of Ministry of Science and Technology (2014DFG72150) and the 111 Project from the Ministry of Education of China (No. B12007).

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  1. Department of Electrical Engineering, Northwest A&F University, Shaanxi, 712100, Yangling, People’s Republic of China

    Sunhua Huang & Bin Wang

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  1. Sunhua Huang
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  2. Bin Wang
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Correspondence to Bin Wang.

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Huang, S., Wang, B. Stability and stabilization of a class of fractional-order nonlinear systems for \(\varvec{0<}\,{\varvec{\alpha }} \,\varvec{< 2}\) . Nonlinear Dyn 88, 973–984 (2017). https://doi.org/10.1007/s11071-016-3288-x

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